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By John, Ph.D. Tabak

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Additional resources for Algebra: Sets, Symbols, and the Language of Thought (The History of Mathematics), Revised Edition

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Brahmagupta was familiar with other approaches to mathematics, but he was motivated by problems that involved difficult calculations. He wanted to find calculating techniques that yielded answers, and he had a very broad idea of what constituted an answer. The Brahma-sphuta-siddha¯nta was quickly recognized by Brahmagupta’s contemporaries as an important and imaginative work. It inspired numerous commentaries by many generations of mathematicians. Mahavira The mathematician Mahavira (ca. 800–ca.

The mathematicians who created this highly imaginative approach to mathematics must have had only a minimal interest in proving that the results they obtained were correct, because mistakes in the texts themselves often went unnoticed. Many of the best Hindu works contain a number of significant errors, but these works also contain important discoveries, some of which have had a profound effect on the entire history of mathematics. Another important difference between Indian mathematics and the mathematics of other cultures with advanced mathematical traditions is that other cultures perceived mathematics as a separate field of study.

His conjecture about the nature of these equations, called Fermat’s last theorem, occupied the attention of mathematicians right up to the present time and was finally solved only recently; we will describe this generalization later in this volume. Today the mathematics for generating all Pythagorean triples is well known but not especially easy to describe. That the mathematicians in the first literate culture in world history should have solved the problem is truly remarkable. Egyptian Algebra Little is left of Egyptian mathematics.

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